Question

what is m∠uvw?
write your answer as an integer or decimal.
m∠uvw =

Explanation:

Step1: Find the measure of ∠WT V

Since \(U T V\) is a straight line, \(\angle U T W+\angle W T V = 180^{\circ}\). Given \(\angle U T W = 117^{\circ}\), then \(\angle W T V=180 - 117=63^{\circ}\).

Step2: Use the property of isosceles triangle

In \(\triangle TWV\), \(TW = TV\) (radii of the same circle). So \(\triangle TWV\) is isosceles, and \(\angle U V W=\frac{1}{2}\angle W T V\) (the base - angle of an isosceles triangle and the property of angles in a circle).

Step3: Calculate \(\angle U V W\)

\(m\angle U V W=\frac{1}{2}\times63 = 31.5^{\circ}\)

Answer:

\(31.5\)